相关论文: Symmetric products, permutation orbifolds and disc…
The theory of permutation orbifolds is reviewed and applied to the study of symmetric product orbifolds and the congruence subgroup problem. The issue of discrete torsion, the combinatorics of symmetric products, the Galois action and…
In this note we point out that a symmetric product orbifold CFT can be twisted by a unique nontrivial two-cocycle of the permutation group. This discrete torsion changes the spins and statistics of corresponding second-quantized string…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…
For a possibly singular complex variety $X$, generating functions of total "orbifold Chern homology classes" of symmetric products $S^nX$ are given. Those are very natural "Chern class versions" (in the sense of Schwartz-MacPherson) of…
We compute the integral cohomology of certain semi-direct products arising from a linear G-action on the n-torus, where G is a finite group. The main application is the complete calculation of torsion gerbes for certain six dimensional…
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories.…
This is a review paper about symmetric products of spaces $SP^n(X):= X^n/S_n$. We focus our attention on the symmetric products of 2-manifolds and make a journey through selected topics of algebraic topology, algebraic geometry,…
Symmetric product orbifold theories are valuable due to their universal features at large $N$. Here we will demonstrate that they have features that are not as pervasive: we provide evidence of strange behaviour under deformations within…
In this paper, we study the symmetry of quantum torus with the concept of crossed product algebra. As a classical counterpart, we consider the orbifold of classical torus with complex structure and investigate the transformation property of…
We construct generalized symmetries in two-dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathcal{T}),$ for a generic seed CFT $\mathcal{T}$. These symmetries are more general than the universal and maximally symmetric ones…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
In this technical note we give a purely geometric understanding of discrete torsion, as an analogue of orbifold Wilson lines for two-form tensor field potentials. In order to introduce discrete torsion in this context, we describe gerbes…
An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…
We develop methods for computing Hochschild cohomology groups and deformations of crossed product rings. We use these methods to find deformations of a ring associated to a particular orbifold with discrete torsion, and give a presentation…
Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…
Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are…
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…
In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we…
We combine our results on symmetric products and second quantization with our description of discrete torsion in order to explain the ring structure of the cohomology of the Hilbert scheme of points on a K3 surface. This is achieved in…